SIGNIFICANCE REGRESSION - A STATISTICAL APPROACH TO PARTIAL LEAST-SQUARES

This paper presents a formal framework for deriving partial least squa res algorithms from statistical hypothesis testing. This new formulati on, significance regression (SR), leads to partial least squares for s calar output problems (PLS1), to a close approximation of a common mul tivariable partial least squares algorithm (PLS2) under certain model assumptions and to more general methods under less restrictive model a ssumptions. For models with multiple outputs, SR will be shown to have certain advantages over PLS2 Using the new formulation, a significanc e test is advanced for determining the number of directions to be used . The prediction and estimation properties of SR are discussed. A brie f numerical example illustrates the relationship between SR and PLS2. (C) 1997 by John Wiley & Sons, Ltd.